Question

верны ли равенства (4√15)(√10-√6)√4-√15=2
√3-√5(3+√5)(√10-√2)=8

Answer 1

$1)quad 4sqrt{15}cdot (sqrt{10}-sqrt6)cdot sqrt{4}-sqrt{15}=\\=4sqrt{15cdot 10}cdot 2-4sqrt{15cdot 6}cdot 2-sqrt{15}=\\=8sqrt{5^2cdot 6}-8sqrt{3^2cdot 10}-sqrt{15}=8cdot 5sqrt6-8cdot 3sqrt{10}-sqrt{15}=\\=40sqrt6-24sqrt{10}-sqrt{15}ne 2$

$2)quad sqrt3-sqrt5(3+sqrt5)(sqrt{10}-sqrt2)=\\=sqrt3-sqrt5(3sqrt{10}-3sqrt2+sqrt{15}-sqrt{10})=\\=sqrt3-3sqrt{50}+3sqrt{10}-sqrt{5cdot 15}+sqrt{50}=\\=sqrt3-15sqrt2+3sqrt{10}-5sqrt3+5sqrt2=3sqrt{10}-4sqrt3-10sqrt2ne 8$